Question: $f(x) = x^2-3x+18 $ What is the value of the discriminant of $f$ ?
Solution: The ${\text{discriminant}}$ is a part of the quadratic formula. The sign of the discriminant tells us whether there are two roots, one root, or no roots. $\dfrac{-b\pm{\sqrt{\overbrace{{b^2-4ac}}^{\text{discriminant}}}}}{2a}$ Discriminant Roots Positive Two real roots Zero One repeated real root Negative No real root Let's find the discriminant of $f$ is given by: $\begin{aligned} {b^2-4ac}&=(-3)^2-4\cdot1\cdot18 \\\\ &=9-72 \\\\ &={-63} \end{aligned}$ So how many real number zeros does $f$ have? Since the discriminant is negative, $f$ has $0$ distinct real number zeros. In conclusion: The discriminant of $f$ is ${-63}$. $f$ has $0$ distinct real number zeros.